Both the HCN/H\(^{13}\) CN and HNC/HN\(^{13}\) C column density ratios display values well below the canonical \(^{12}\) C/\(^{13}\) C elemental abundance ratio in the ISM, equal to 68 [1]}, [2]}. In particular, a low \(^{12}\) C/\(^{13}\) C ratio of \(\approx 11\pm 4\)  is measured towards towards the cold protostellar core L1157-mm. We first note that models of \(^{13}\) C isotopic fractionation in cold cores lead to an opposite effect, i.e. a H\(^{12}\) CN/H\(^{13}\) CN (HN\(^{12}\) C/HN\(^{13}\) C) ratio higher than the \(^{12}\) C/\(^{13}\) C elemental abundance ratio [3]}, [4]}.
A similar effect was reported by citetDaniel2013 in their detailed study of nitrogen hydrides and nitriles in the Class 0 protostellar core Barnard 1. The authors concluded that the apparently low H\(^{12}\) CN/H\(^{13}\) CN ratio was most likely a bias caused by the simple hypothesis made in the radiative transfer modelling of the line excitation and the geometry of the astrophysical source. In particular, the excitation of the HCN and HNC ground-state transitions also depends on the extended, low-density gas surrounding the dense core, so that a detailed multi-dimensional radiative transfer model of the source taking into account the full density and velocity fields is needed in order to properly reproduce the line profiles .
